Backstep Flow Research Articles

The reduced-order method of continuous space-time finite element scheme for the non-stationary incompressible flows

In this paper, we mainly concern with the order reduction for the unknown solution coefficient vectors about the classical continuous space-time finite element (CCSTFE) method of the two-dimensional (2D) non-stationary incompressible Navier-Stokes equations. Therefore, we first build the CCSTFE scheme for the 2D non-stationary Navier-Stokes equations with respect to stream–vorticity functions, give the existence and stability together with convergence to the CCSTFE solutions, and rewrite the CCSTFE scheme as a matrix form. And then, we use a proper orthogonal decomposition (POD) technique to build a reduced-order extrapolated continuous space-time finite element (ROECSTFE) scheme in the matrix form including very few unknowns but possessing high enough accuracy, employ matrix analysis to demonstrate the existence and stability together with convergence of the ROECSTFE solutions such that the theoretical analysis becomes very concise and convenient, and summarize the flowchart for solving the ROECSTFE scheme. Finally, we take advantage of the numerical simulations for the back-step flow and the flow around airfoil problem to verify the correctness of theoretical results.

周期的かく乱を伴う３次元ダクト内バックステップ下流の熱流動特性

The flow and heat transfer characteristics were investigated by numerically simulating backstep flow in a three-dimensional duct with periodic disturbance to the inlet velocity at moderate Reynolds numbers (Re = 625, 700, and 1000). The periodic disturbance was applied to the approximate equation for a well-developed flow by varying the relative amplitude and forcing frequency. The results show that the reattachment position moves upstream as the disturbance increases. Furthermore, as the Reynolds number increased, the amount of change in the reattachment position due to the disturbance became smaller. This change in the reattachment position was more dependent on the forcing frequency than on the relative amplitude, because the meander spacing of the mainstream narrowed as the forcing frequency increased. The spatiotemporally averaged Nusselt number at each Reynolds number increased by 27.2% when a disturbance was applied, compared to the case where no disturbance was applied. This is due to the fact that the higher the disturbance, the more active the heat exchange becomes not only in the flow direction but also in the height direction, resulting in a higher rate of rise. As with the reattachment position, the amount of change became smaller as the Reynolds number increased. These results suggest that the use of the disturbance can be expected to enhance heat transfer at the lower wall.

Transient simulation and experiment validation on the opening and closing process of a ball valve

The ball valve is an important device in the pipeline transportation system of nuclear power plants. Its operational stability and safety directly affect the normal working of nuclear power plants. In this study, the transient numerical simulation of the opening and closing process of a ball valve was conducted on the basis of the flow interruption capability experiment of the ball valve by using the moving mesh method and inlet and outlet variable boundary conditions. The flow rate and pressure difference with time of the opening and closing process of the ball valve were studied. The internal flow characteristics of the ball valve under different relative openings were analyzed in conjunction with the typical back-step flow structure. Results show that the transient numerical results agree well with the experimental results. The internal flow characteristics of the ball valve are similar at the same opening during opening and closing process. At small opening, the spool and outlet channels easily form a back-step flow structure. The disappearance and generation of backflow vortices during opening and closing occur at 85% opening and 75% opening, respectively. With the decrease in opening degree, the difference in vortex core area in the flow channel of the ball valve spool in the opening and closing process gradually appears. The research results provide some reference value for the design and optimization of ball valves.

Numerical Forced Convection Heat Transfer of Nanofluids over Back Facing Step and Through Heated Circular Grooves

Backward facing step arrangement is a classical case for fluid dynamics and heat transfer research. It is well characterized and therefore, used for benchmarking. However, ongoing studies reveal that the geometry also provide advantages in industry, especially in combustion and burners. This work utilizes computational fluid dynamics to investigate a specific laminar back facing step flow heat transfer case. Aluminium oxide nano particles are considered as an additive to water base fluid, forming nanofluid with different volumetric concentrations. Laminar flow passes a back facing step and encounters three circular grooves at bottom surface. All surfaces are adiabatic except the grooves. Constant surface temperature applies to the grooves. According to the simulation results, a separation bubble after back facing step and a reattachment point occur. Grooves alter expected wake due to physical and thermal interference. Investigation parameters are nano-particle concentration and Reynolds number. Reynolds number changes between 10 and 250. Nano particle volume fraction percentage changes between 2 and 6 percent. Sectional heating downstream of the step poses interesting heat flux in the presence of Aluminium oxide nano-particle concentrations. There is a pseudo-linear relationship between parameters and heat transfer. Combined effects of enhanced thermal conductivity and secondary flow structures are seen. As expected, thermal convection increases as flow velocity and nano-particle concentrations increase. Heat flux and accordingly Nusselt number are highly affected from Reynolds number since flow structure changes dramatically. Also, direct proportion is seen between nano-particle concentration and enhanced convection.

An extensive numerical benchmark of the various magnetohydrodynamic flows

There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.

Burning rate augmentation in solid fuel ramjets by swirling inlet air stream

The influence of the inlet swirling flow on the regression rate of the fuel in the combustion chamber of the solid fuel ramjet is investigated in this study using numerical simulations. The finite-volume solver of the compressible turbulent reacting flow is developed to study the flow field where the burning rate is computed using the conjugate heat transfer method for the solid fuel. The correlation is found for the maximum regression rate versus an imposed inlet swirl when the linear distribution of the circumferential velocity is applied at the inlet stream. Although the regression rate augmentation is considerable due to the swirling flow field in the combustor, it is shown that the swirl is effective if is applied near the shear layer of the backstep flow in the combustor. The modified swirler with short blades is suggested to be used in solid fuel ramjets to increase the regression rate of the fuel and improve the performance, but with lower pressure loss.

Upward bubbly flows in a square pipe with a sudden expansion: Bubble dispersion and reattachment length

We investigate the bubble dynamics and subsequent changes in the liquid-phase flow characteristics of upward bubbly flows in a square pipe with a sudden expansion (expansion ratio of 4.0). The experiments are conducted under three liquid-phase Reynolds numbers of 0 (stationary), 420 (laminar) and 6000 (turbulent). The inlet volume void fraction ranges about 0−1.0%, and we use a high-speed two-phase particle image velocimetry and shadowgraphy to measure two phases simultaneously. It is observed that after the expansion, smaller bubbles tend to migrate toward the wall and larger bubbles rise in a core region, which is more encouraged by the steeper velocity gradient with increasing the Reynolds number. This bubble distribution is further analyzed by estimating the interfacial forces acting on rising bubbles. Affected by this bubble distribution, the enhanced turbulence in the inlet flow energizes the separating shear layer, resulting in the reduction of reattachment length behind the edge. Finally, we suggest an empirical relation for a two-phase flow reattachment length in terms of Reynolds number and mean void fraction, which explains the contribution of added dispersed phase on the mixing enhancement in the backstep flows.

2D Back-Step Flow Simulation by Immersed Boundary Method

2D Back-Step Flow Simulation by Immersed Boundary Method

A model for heating and evaporation of a droplet cloud and its implementation into ANSYS Fluent

A model for heating and evaporation of a cloud of monocomponent droplets in air, taking into account the evolution of droplet number densities, is developed and implemented into ANSYS Fluent. Functionality testing of the new customised version of ANSYS Fluent is based on its application to the analysis of a droplet cloud in a two-phase back-step flow. It is shown that the effect of the droplet cloud needs to be taken into account when estimating the heat and mass transfer rates from the carrier phase to the droplets.

Boundary conditions for lattice Boltzmann method with multispeed lattices

Boundary methods and boundary node treatments for a multispeed lattice are presented in detail for incompressible isothermal flows, which remain a challenging application of the lattice Boltzmann method. We developed a completely generic way of handling boundaries with known velocity for multispeed lattices by extending and improving the on-site boundary conditions proposed by Hecht et al. [1], which was only intended for single speed lattice. In addition, we studied two ways of treating the unknown distribution functions that span several layers of nodes, namely, the external treatment (the inner layer is the boundary) and the internal treatment (the outermost layer is the boundary). The external treatment requires the use of ghost nodes at the boundary, whereas the internal treatment relies on an interpolation technique. The external treatment is found to offer more stability than the internal treatment when an open boundary condition is involved. The improved on-site boundary method for multispeed lattices is shown to be local, second-order accurate. Numerical validation is demonstrated with classical benchmark problems, namely, lid-driven square cavity, channel, and back-step flows, at different Reynolds numbers and grid resolutions.

Turbulent heat transfer past a sudden expansion with a porous insert using a nonlinear model

ABSTRACTThis work presents numerical investigations for turbulent flow and heat transfer in a backward-facing step with and without porous inserts. Two classes of the model were employed, namely linear and nonlinear turbulence closures. The entire set of transport equations was discretized by means of the control volume method and the system of algebraic equations obtained was relaxed using the SIMPLE (Semi Implicit Pressure-Linked Equations) method. Results were first validated against the experimental data and the simulations follow experimental values and trends. Computations further indicated that when using the porous insert, the size, shape, and length of the recirculating region were drastically reduced in addition to being pushed toward the channel exit, leading eventually to a complete bubble suppression for thicker inserts. A more permeable medium gave better results in quickly suppressing the circulatory motions. By including porous inserts in the channel, turbulence generated due to the shear inside the recirculating region was damped, whereas high levels of k were concentrated within the permeable structure. Large variations for the skin friction factor along the bottom wall were also smoothed out by placing inserts, spanning from a typical distribution for an unobstructed back-step flow to a standard parallel channel flow distribution as the inserts got ticker. On the other hand, at the upper wall, flow pushed toward the top surface gave rise to a sudden increase of the skin friction factor, which was later stabilized downstream the flow. Heat transfer analysis followed showing damping for Nu at the bottom wall as the thickness of the porous substrate was increased. Overall, the thickness of the insert played a dominant role in changing the final flow and heat transfer characteristics rather than the porosity or permeability of the porous material. Finally, this work indicated that the sudden increase of Nu around the reattachment point, known to be undesirable in many practical situations for causing additional thermomechanical loads on the surface, may by avoided by the use of a porous obstacle past the back-step.

A modified turbulent heat-flux model for predicting heat transfer in separating-reattaching flows and film cooling applications

The present study addresses a new effort to improve the prediction of the thermal field in separating-reattaching flows by making modifications in a low-Reynolds-number (LRN) version of HOGGDH heat-flux model proposed by Suga and Abe (2000). The modifications are based on introducing non-equilibrium effects of hydrodynamic flow field in the heat-flux model. Using an analytical approach, we have implemented P/ε, ignored in the base version, to the modified version. To do so, the model structure was changed and a damping function which is more sensitive to non-equilibrium flow features is also applied to the model. The modified heat-flux formulation along with a second moment closure hydrodynamic model is validated in a backstep flow, a periodic ribbed duct flow and a 3D high-blowing-ratio film cooling flow. Promising results are obtained compared with GGDH and HOGGDH models and the model performance is found to be comparable to θ2¯-εθ heat models, but with less computational and implementational complexity. For the film cooling flow, the rapid cooling efficiency drop due to the jet lift-off is accurately predicted though some margins to be improved still remain.

Dynamic characterization of piezoelectric micro-blowers for separation flow control

A micro-blower device, made by Murata™ Manufacturing Co. and originally designed for cooling electronic microprocessors, is used in the present study as an actuator for separation flow control. The dynamical performance of the device, working in pulsed mode, is experimentally investigated to deduce its abilities and limitations regarding active flow control. Both the device design and its dynamical characterization are addressed in the paper, paying particular attention to its ability to control flow. Both hot-wire anemometry and particle image velocimetry have been employed to investigate the dynamical evolution of the pulsed jet and allow the identification of the jet organized flow structures. The phase-averaging technique is applied to distinguish the large scale structure dynamics induced during the ejection phase. An array of active devices is also used to evaluate the flow control efficiency by forcing frequency strategy in order to reduce the separation area of a back facing step flow. Results show good performance in open loop flow control and applicability of such actuator for further closed loop flow control research.

Large-eddy simulations of gas- and liquid-fueled combustion instabilities in back-step flows

LES of gas and spray combustion in back-step flows are performed to investigate the mechanism underlying combustion instability and the effect of initial droplet diameter on combustion instability. Methane and kerosene are used as fuel for gas and spray combustion, respectively, and two-step global reaction models are used for the reactions. A dynamic thickened flame model is employed as the turbulent combustion model. The motions of evaporating droplets are tracked using the Lagrangian manner. The results show that in gas combustion, the pressure, heat release rate and streamwise velocity oscillate with the same frequency but different phases, and that the inlet velocity oscillation periodically generates a large vortex near the dump plane that drives combustion instability. In spray combustion, an oscillation of droplet evaporation rate is also observed. Whereas the difference in the initial droplet diameter slightly affects the mode of the pressure oscillation, it strongly affects the intensity of the pressure oscillation and causes a maximum value for a specific initial droplet diameter. This arises from the difference in the initial droplet diameter causing a difference in the droplet evaporation rate, which alters the relationship between the oscillations of the heat release rate and pressure near the dump plane.

Heat transfer enhancement of backstep flow by means of EHD conduction pumping

Electrohydrodynamics (EHD) conduction pumping takes advantage of the electrical Coulomb force generated by externally applied electric field and dissociated charges from electrolytes. The backstep flows that appear in certain types of MEMS application are not very efficient from the heat transfer standpoint due to the trapped circulation flow in the reattachment zone. This paper is a numerical study on the application of EHD conduction pumping as an auxiliary tool for heat transfer enhancement of backstep flows in macro- and micro-scale systems. An innovative electrode design with a dc electric potential difference is proposed with the primary motivation to reduce the volume of reattachment zone.

An analytical wall-function for recirculating and impinging turbulent heat transfer

The performance of the analytical wall-function (AWF) of Craft et al. [Craft, T.J., Gerasimov, A.V., Iacovides, H., Launder, B.E., 2002, Progress in the generalisation of wall-function treatments. Int. J. Heat Fluid Flow 23, 148–160.] is improved for predicting turbulent heat transfer in recirculating and impinging flows. Since constant parameters of the eddy viscosity formula were used to derive the AWF, the prediction accuracy of the original AWF tends to deteriorate in complex flows where those parameters need changing according to the local turbulence. To overcome such shortcomings, the present study introduces a functional behaviour on the strain parameter into the coefficient of the eddy viscosity of the AWF. The presently modified version of the AWF is validated in turbulent heat transfer of pipe flows, channel flows, back-step flows, pipe flows with abrupt expansion and plane impinging slot jets. The results confirm that the present modification successfully improves the performance of the original AWF for all the flows and heat transfer tested.

Piloted ignition of solid fuels in turbulent back-step flows

Piloted ignition of solid fuels in dump combustor geometry subject to an igniter hot jet plume is numerically investigated. The objective of this work is to gain insight into the fuel ignition and subsequent flame spreading in this turbulent flow configuration. Conjugate heat transfer between gas and solid phases is considered to study the solid fuel heating and evaporation process; Solid phase energy equation is simultaneously solved coupled with flow governing equations. Finite rate one step second order chemistry is used in simulations. The gas phase equations along with the Spalart–Allmaras turbulence model are solved with a finite volume approach in which the AUSM+ scheme is used to calculate the convective fluxes. The overall ignition delay time and flame spreading rate are predicted under a typical igniter operation. The results show that choosing a stronger igniter for reducing the ignition delay time does not necessarily guaranty the perfect firing process.

Robust reduced order modeling of heat transfer in a back step flow

We present a method to obtain reduced order models to calculate steady states in thermal systems of industrial interest. The method could be regarded as an evolution of the standard proper orthogonal decomposition (POD) method, in which the reduced model is obtained through standard Galerkin projection (whose application exhibits well known difficulties) on previously obtained POD modes. Instead of relying on a Galerkin projection, we use a genetic algorithm (GA) to minimize a conveniently defined residual for the (continuity, momentum, and energy) equations and boundary conditions. The method and its practical application are illustrated on a test problem that describes heat transfer in the recirculation region downstream of a backwards facing step.

Experimental study of fluid flow and heat transfer characteristics in the square channel with a perforation baffle

This work performed a detailed measurement of local heat transfer coefficients in a square channel with a perforation baffle by using the transient liquid crystal themography. The varied parameters were the Reynolds number, the baffle height, and the hole numbers on the perforation baffle. The results showed that the enhancements of local heat transfer appeared in the leading edge of the baffle due to the impinging effect, which was more significant when Reynolds number became larger or the baffle height became higher. Additionally, the heat transfer coefficients off center were better than those in the center at downstream of the baffle. It might be resulted from two secondary flows, which appeared off center after the airflow passed through the baffle. Baffles with various hole numbers but having same total hole area were also studied to find the heat transfer enhancement. The results depicted that the back facing step flow which had characteristics of backflow and flow reattachment had an important effect on the heat transfer characteristics at downstream of the baffle. Finally, the correlation for the location of the flow reattachment point ( X r) was proposed.

A code-independent technique for computational verification of fluid mechanics and heat transfer problems

The goal of this paper is to present a versatile framework for solution verification of PDE’s. We first generalize the Richardson Extrapolation technique to an optimized extrapolation solution procedure that constructs the best consistent solution from a set of two or three coarse grid solution in the discrete norm of choice. This technique generalizes the Least Square Extrapolation method introduced by one of the author and W. Shyy. We second establish the conditioning number of the problem in a reduced space that approximates the main feature of the numerical solution thanks to a sensitivity analysis. Overall our method produces an a posteriori error estimation in this reduced space of approximation. The key feature of our method is that our construction does not require an internal knowledge of the software neither the source code that produces the solution to be verified. It can be applied in principle as a postprocessing procedure to off the shelf commercial code. We demonstrate the robustness of our method with two steady problems that are separately an incompressible back step flow test case and a heat transfer problem for a battery. Our error estimate might be ultimately verified with a near by manufactured solution. While our procedure is systematic and requires numerous computation of residuals, one can take advantage of distributed computing to get quickly the error estimate.